We propose a scheme to cool down a mechanical resonator to its quantum ground-state, which is interacting with a cavity mode via the optomechanical coupling. As opposed to standard laser cooling schemes where coherence renders the state of the resonator to its ground-state, here we use incoherent thermal light to achieve the same aim. We show that simultaneous cooling of two degenerate or near-degenerate mechanical resonators is possible in our scheme, which is otherwise a challenging goal to achieve in optomechanics. The generalization of this method to the simultaneous cooling of multiple resonators is straightforward. The underlying physical mechanism of cooling is explained by revealing a direct connection between the laser sideband cooling and “cooling by heating” in a standard optomechanical setting.